Aprofessional race-car driver buys a car that can accelerate at 5.2 m/s2 . the racer decides to race against another driver in a soupedup stock car. both start from rest, but the stock-car driver leaves 1.3 s before the driver of the sports car. the stock car moves with a constant acceleration of +3.2 m/s2 . find the time it takes the sports-car driver to overtake the stock-car driver. answer in units of s.

6.02 s

Explanation:

We can write the position of the stock car as:

where

is the acceleration of the stock car.

The sport car instead starts its motion only 1.3 s afterwards, therefore its position at time t can be written as

where

is the acceleration of the sport car

(we can verify indeed that when t = 1.3 s, ).

The sport car reaches the stock car when the two positions are equal:

Rewriting the equation,

This is a second-order equation with two solutions:

t = 0.73 s

t = 6.02 s

We discard the first solution since we are only interested in the times > 1.3 s, therefore the sport car overcomes the stock car after

6.02 seconds.