Question

How long will it take a car, starting from rest, accelerating at 2 meters per second square to travel the same distance that another car traveling at a constant rate of 20m/s will travel?

Answer 1

20 seconds

Step-by-step explanation:

Let
`x_a` be the distance traveled by the accelerating car and
`x_c` be the distance traveled by the car moving with a constant velocity. When they cover the same distance, we can write

`x_a = x_c \Rightarrow v_(0a)t + (1)/(2)at^2 = v_ct`

where
`v_c` is the velocity of car moving at a constant rate and a is the acceleration of the accelerating car. Since the accelerating car started from rest, then
`v_(0a)` is zero so our equation above simplifies to

`(1)/(2)at^2 = v_ct`

Note that the variable t cancels out so solving for t, we get

`(1)/(2)at = v_c \Rightarrow t = (2v_c)/(a)`

Plugging in the given values,

`t = \frac{2(20\:\text{m/s})}{2\:\text{m/s}^2} = 20\:\text{s}`