Question

A toy car, initially travelling in a straight line at 30.0 cm/s, slows down with a constant linear acceleration of 3.0 cm/s2. How much time passes before the toy car comes to a halt?

Answer 1

Answer:

The toy car stops after 10 seconds.

Explanation:

Constant Acceleration Motion

It's a type of motion in which the velocity of an object changes uniformly at a rate called acceleration.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:

$v_f=v_o+at\qquad\qquad [1]$

The toy car moves at vo=30 cm/s and decelerates at $a=-3\ cm/s^2$. Note the negative sign of the acceleration that indicates the speed is decreasing over time.

We need to calculate the time needed for the toy car to stop vf=0.

To find the time, we solve [1] for t:

$\displaystyle t=\frac{v_f-v_o}{a}$

Since all the units of speed and acceleration are in centimeters, we don't need to convert to meters

$\displaystyle t=\frac{0-30}{-3}=10$

The toy car stops after 10 seconds.