Honors Physics: Kinematics

equations, questions, and concepts

Does a car speedometer measure speed, velocity, or both?

speed because there is no direction present

Can an object have a varying speed if its velocity is constant?

No. Varying velocity means varying speed. In a circular path, speed can be constant with varying velocity (but not the other way around)

T or F: average velocity is less than or equal to average speed

True. Remember absolute value of velocity is equal to speed

How is distance as a function of time expressed?

x = (avg v)(t) + Xo

How is velocity as a function of time expressed?

v = at + Vo

How is distance as a function of time that includes acceleration expressed?

delta x = Vo(t) + ½ (a)(t)²

What’s a kinematic equation we can use if time isn’t given?

V² = (Vo)² + 2a(delta x)

Compare the acceleration of a motorcycle that accelerates from 80 km/h to 90 km/h with the acceleration of a bicycle that accelerates from rest to 10 km/h in the same time.

Their accelerations are equal. acceleration is change in velocity over time, and the time and velocity are the same for both the motorcycle and bike

You travel from A to B moving at a constant speed of 70 km/h. You travel to B to C at a constant speed of 90 km/h. The distance from A to B is the same from B to C. Is your average speed from A to C going to be 80 km/h?

No. You take longer traveling from A to B than from B to C (since you’re slower).

Average speed for the first segment will be x/70 (distance over time = avg. speed). For the second one, it’s x/90.

Add the two fractions together to get your total time. Then, do total distance (2x) over your time to get final average speed.

Can an object have zero velocity and nonzero acceleration at the same time?

Yes. When you throw a ball in the air, it has zero velocity when it reaches the top of its trajectory, but it still has acceleration.

In calculus, a velocity graph can reach zero; but the acceleration (it’s derivative) might be something else

A car traveling 88 km/h is 110m behind a truck traveling 75 km/h. How long will it take the car to reach the truck?

use v = displacement/time

13 = 0.11/t , solve for t

multiply t (in hours) by 3600 to get seconds

answer: about 30.46 seconds

A car accelerates from 13 m/s to 25 m/s in 6 seconds. What was its acceleration? How far did it travel in this time? Assume constant acceleration.

Find acceleration first using v = a(t) + initial velocity:

25 = a(6) + 13, a = 2 m/s²

Find displacement using:

delta x = Vo(t) + ½ a(t)²

13(6) + ½ (2)(6)² = 114m

A car traveling 85 km/h strikes a tress. The front end of the car compresses and the driver comes to rest after traveling 0.8m. What was the average acceleration o the driver during the collision? Express the answer in terms of g’s (1.00g = 9.8m/s²)

Use v² = (Vo)² + 2a(delta x)

85² = 2a(0.0008) **I converted 0.8m to 0.0008km.

a = 451625 km/h²

do some dimensional analysis to get:

a = 7.87 × 10^-6 g