Question

A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 19.0m/s , and the distance between them is 52.0m . After t1 = 5.00s , the motorcycle starts to accelerate at a rate of 5.00m/s^2. a. How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words. b. Find t2−t1

Answer 1

Answer:

$t\approx4.561\ s$

Explanation:

Given:

• initial speed of car and motorcycle, $v=19\ m.s^{-1}$

• initial distance between the car and motorcycle, $s=52\ m$

• time after which the motorcycle starts to accelerate, $t_1=5\ s$

• rate of acceleration of motorcycle, $a=5\ m.s^{-2}$

The initially the relative velocity of the motorcycle is zero with respect to car.

Now using the equation of motion in the relative quantities:

$s=u.t+\frac{1}{2} .a.t^2$

here:

$s =$ relative distance of motorcycle with respect to the car

$u=$ initial relative velocity of the motorcycle with respect to the car

$t=$ time taken to cover the distance gap from the car.

$52=0+0.5\times 5\times t^2$

$t\approx4.561\ s$