# Worksheet: Average and Instantaneous Acceleration

In this worksheet, we will practice calculating instantaneous acceleration as the rate of velocity change in a time interval that approaches zero.

**Q8: **

The velocity of a particle moving along the -axis varies with time according to , where , , and s. At , .

Determine the acceleration of the particle at .

Determine the acceleration of the particle at .

Determine the displacement from of the particle at .

Determine the displacement from of the particle at .

**Q10: **

A light-rail commuter train traveling in a straight line accelerates at a rate of 1.93 m/s^{2}.

How much time is required for the train to reach a speed of 74.0 km/h?

If the train is traveling at 74.0 km/h and decelerates to rest at a rate of 1.18 m/s^{2}, how much time passes before the train stops?

The train can decelerate more rapidly in emergencies, coming to rest from 74.0 km/h in 11.3 s. What is the emergency acceleration rate?

**Q12: **

A particle that is in motion has a changing velocity that is modeled by the function m/s.

Find the instantaneous velocity of the particle at .

Find the instantaneous velocity of the particle at .

Find the instantaneous velocity of the particle at .

Find the instantaneous velocity of the particle at .

Find the instantaneous acceleration of the particle at .

Find the instantaneous acceleration of the particle at .

Find the instantaneous acceleration of the particle at .

Find the instantaneous acceleration of the particle at .

**Q16: **

On dry concrete, a car can decelerate at a rate of
7.00 m/s^{2}, whereas
on wet concrete it can decelerate at only 5.00 m/s^{2}. The car has an initial velocity of
30.0 m/s. The
car’s stopping distance is the distance that it travels before coming to rest
from its initial velocity. The stopping distance is affected by the driver’s
reaction time, which is the time interval between the driver making the decision to
apply the car’s brakes and moving her foot to apply them. The driver’s
reaction time is 0.500 s.

What is the car’s stopping distance on dry concrete, neglecting the driver’s reaction time?

What is the car’s stopping distance on wet concrete, neglecting the driver’s reaction time?

What is the car’s stopping distance on dry concrete?

What is the car’s stopping distance on wet concrete?

**Q19: **

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart’s velocity as a function of time is shown in the graph. The five labeled points divide the graph into four sections. Which of the following correctly ranks the magnitude of the average acceleration of the cart during the four sections of the graph?

- A
- B
- C
- D