A bike travels at 7.5 m/s along a straight road, whereas a car travels at 10.0 m/s along the same road and in the same direction
. When the car is 5.0 m ahead of the bike, it starts slowing down at a constant rate of 0.75 m/s^2 . a) How long it will take the bike to reach the car, and at what location (relative to its position when the car began slowing down) is the bike then? b) Plot the positions of the car and the bike as functions of time.
1 answer:
You might be interested in
a = 3.09 m/s²
<h3>Explanation</h3>This question doesn't tell anything about how long it took for the car to go through 105 meters. As a result, the <em>timeless </em>suvat equation is likely what you need for this question.
In the <em>timeless</em> suvat equation,
where
is the acceleration of the car;
is the <em>final</em> velocity of the car;
is the <em>initial</em> velocity of the car; and
is the displacement of the car.
Note that <em>v</em> and <em>u</em> are velocities. Make sure that you include their signs in the calculation.
In this question,
;
; and
.
Apply the <em>timeless</em> suvat equation:
.
The value of is greater than zero, which is reasonable. Velocity of the car is negative, meaning that the car is moving backward. The car now moves to the back at a slower speed. Effectively it accelerates to the front. Its acceleration shall thus be positive.