GENERAL MOTION NOTES

When do you use differentiation?

When you can’t use SUVAT if acceleration is not constant

What is velocity?

What is acceleration?

Velocity = rate of change of displacement with respect to time, v = ds/dt

Acceleration = rate of change of velocity with respect to time, a = dv/dt

Between velocity, acceleration and position, state the order at which you differentiate

What about integrate?

Position → velocity → acceleration

• Integration is the opposite

EXAMPLE: The position of a particle after t seconds is given by s = t³ - 5t² + 7t - 3

A) Find an expression for the velocity at time t

B) Find the velocity after 3 seconds

C) Find an expression for the acceleration

A) v = ds/dt = 3t² - 10t + 7

B) 3(3)² - 10(3) + 7 = 4 m/s

C) a = 6t - 10

EXAMPLE: a particle, initially at rest at the point where s=3, has an acceleration at time t seconds given by a = t³ - 2t²

• Find an expression for its velocity at time t

• Find an expression for its position at time t

• V = ¼ t⁴ - 2/3 t³ + c

  0 = ¼ (0)⁴ - 2/3 t³ + c

  C = 0

  ANS = V = ¼ t⁴ - 2/3 t³

• S = 1/20 t⁵ - 1/6t⁴ + c

  3 = 1/20(0)⁵ - 1/6(0)⁴ + c

  C = 3

  ANS = S = 1/20 t⁵ - 1/6t⁴ + 3

GO DO QUESTIONSSSS

GOOOOO