Question

9. A car is driving down the road at 15 m/s when the driver notices a stop sign up ahead. The driver applies the brakes and comes to a stop in 5 seconds. What was the acceleration of the car when the brakes were applied?

10. A rock drop-off 1250 feet building, has height s (in feet) above the ground at time t seconds given by s (t) = 1250 - 16t2. What is the instantaneous velocity of the rock at 5 seconds?

11. A particle is in motion and is accelerating. The functional form of the velocity is v (t) = 20t - 5t2. Find the instantaneous acceleration at t = 3 seconds.

12. You are riding your bike downtown at a speed of 15 m/s and you see a red light ahead. You gently brake over a distance of 50 m and come to a complete stop. What is your acceleration during this time?

Answer 1

9. The acceleration:

$$a=v/t=15/5=3\text{ m/s}^2.$$

10. The instantaneous velocity:

$$v(t)=\text ds(t)/\text d t=-32t,\\\space\\ v(5)=-160\text{ ft/s}.$$

11. The acceleration:

$$a(t)=v'(t)=20-10t,\\\space\\ a(3)=-10\text{ m/s}^2.$$

12. The acceleration is

$$a=v^2/(2d)=2.25\text{ m/s}^2.$$