7.2 + 7.3 + 7.6 - acceleration

what is acceleration?

the change of velocity per unit time

the acceleration is the change of what?

change of velocity per unit time

the accleration is the change of velocity per what?

the acceleration is the change of velocity per unit time

what is the change of velocity per unit time?

acceleration

what is the symbol for acceleration?

a

what is the unit for acceleration?

metres per second squared (m s^-2)

is acceleration a vector or scalar quantity?

a vector quantity

why is acceleration a vector quantity?

because it has a magnitude and direction

why is deceleration negative?

to signify the velocity decreases with respect to time

what is a velocity-time graph?

here

• y axis = velocity

• x-axis = time

• gradient = acceleration

• area under graph = displacement

what is the y-axis of a velocity-time graph?

velocity

what is the velocity on a velocity-time graph?

y-axis

what is the x-axis of a velocity-time graph?

time

what is the time on a velocity-time graph?

x-axis

what is the gradient of a velocity-time graph?

acceleration

what is the acceleration on a velocity-time graph?

gradient

what is the area under a velocity-time graph?

displacement

what is the displacement on a velocity-time graph?

displacement

what is a velocity-time graph when accleration is constalty increasing?

here

gradient is a straight line with positive gradient

velocity-time graph when acceleration is constantly increasing here

velocity-time graph when acceleration is constantly increasing

what is a velocity-time graph when accleration is constalty decreasing?

here

gradient is a straight line with negative gradient

velocity-time graph when acceleration is constantly decreasing here

velocity-time graph when acceleration is constantly decreasing

what is a velocity-time graph when there is no acceleration?

here

gradient is 0

velocity-time graph when there is no acceleration here

velocity-time graph when there is no acceleration

what do we use for constant acceleration?

• SUVAT

• velocity-time graphs

what do we use for non-uniform acceleration?

velocity-time graphs

when do we use a velocity-time graph?

when acceleration is either uniform or non-uniform

when do we use suvat?

when acceleration is constant

what is uniform / constant acceleration?

where the velocity of an object moving along a sftraight line changes at a consant rate

what kind of motion does uniform acceleration apply to?

motion in a straight line

how do you find constant acceleration on a velocity-time graph?

• gradient = change in y / x

• acceleration = change in velocity / time taken

• a = (v - u) / t

a = (v - u) / t

constant acceleration, gradient of a velocity-time graph at constant acceleration

derive v = u + at

• gradient of velocity-time graph = acceleration = (v - u) / t

• rearranged gives v = u + at

what is non-uniform acceleration?

where the direction of motion of an object changes, or its speed changes, at a varying rate

what is the acceleration of an object when the direction of motion changes?

non-uniform

what is the acceleration of an object when its speed changes?

non-uniform

what is the velocity-time graph for an object moving at non-uniform acceleration?

curved gradient

here

what is the gradient of a velocity-time graph moving at non-uniform acceleration?

curved

here

where do velocity-time graphs start from?

the origin

velocity-time graph of an object moving at non-uniform acceleration here

velocity-time graph of an object moving at non-uniform acceleration

how do you find the acceleration of an object moving at non-uniform acceleration on a velocity-time graph?

• drawing a tangent on any point of the curve

• draw a gradient traingle from the tangent

• find the gradient of the gradient triangle - height of gradient triangle / base of gradient triangle

here

what is a gradient traingle?

here

how do you find the gradient of a gradient triangle?

height of gradient triangle / base of gradient triangle

why is accerelation non-uniform if either its direction of motion or speed changes?

because acceleration is a vector quantity that depends on both speed and direction

what are the SUVAT equations?

• a = (v - u) / t

• v = u + at

• s = (u + v) t / 2

• s = ut + ½ a t²

• v² = u² + 2 a s

derive s = (u + v) t / 2

• s = average velocity x time

• accerleration is uniform

• so average velocity = (u + v) / 2

• s = v t

• s = (u + v) t / 2

derive s = ut + ½ a t²

• s = (u + v) t / 2

• v = u + a t

• s = (u + (u + a t)) / 2

• t = (u + u + a t) t /2

• t = (2 u t + a t²) / 2

• s = u t + ½ a t²

derive v² = u² + 2 a s

• a = (v - u) / t

• s = (u + v) t / 2

• a s = ((v - u) / t) x ((u + v) t / 2)

• 2as = v² - u²

• v² = u² + 2 a s

what is acceleration when velocity is constant?

how do you find the displacement of this velocity-time graph of an object moving at constant velocity?

here

• displacement = area under graph

• rectangle of height v and base t

• s = v t

here

velocity-time graph of object moving at constant velocity here

velocity-time graph of object moving at constant velocity

what is a velocity-time graph when object is moving is moving at a constant velocity?

acceleration = gradient = 0

how do you find the displacement of this velocity-time graph of an object moving at constant acceleration?

here

• area under graph = trapezium

• area of trapezium = ½ (b + a) x h

• = ½ (u + v) x t

• ½ (u + v) t

here

what is the area of a trapezium?

½ (b + a) x h

here

½ (u + v) t

displacement of object moving at constant acceleration on a velocity-time graph

velocity-time graph of an object moving at changing acceleration here

velocity-time graph of an object moving at changing acceleration

what is a velocity-time graph of an object moving at changing acceleration?

here

curved gradient

how do you find the displacement of an object moving at changing acceleration using a velocity-time graph?

• take strips under the graph, each of the same width

• total displacement = total area under line = sum of the area of each strip

• area of each strip = change in displacement in that strip = vΔt

what is the area of each strip of the velocity-time graph of an object moving at a changing acceleration?

vΔt

here

why is the area of each strip of the velocity-time graph of an object moving at constant acceleration vΔt?

here derivation idk

how do we resolve directions in SUVAT?

• one direction is positive, another is negative

• as SUVAT deals with motion along a straight line, we only need to consider those two directions

what is a two-stage problem?

SUVAT equations with two stages of movement, each with a different acceleration

for a two-stage problem, what is the acceleration?

different in each stage of motion

for a two-stage problem, what is the velocity?

initial velocity of second stage of motion = final velocity of first stage of motion