Question

A stuntman drives a car of mass 1125 kg east with a speed of 20 m/s.

a. If the car accelerates at a rate of -2 m/s², how long will it take the car to go 50 m?
A. 5 s
B. 10 s
C. 25 s
D. 50 s

Answer 1

The stuntman's car will take 10 seconds to travel 50 meters east when accelerating at a rate of -2 m/s², given the initial velocity of 20 m/s.

Step-by-step explanation:

Calculating Time for a Car to Travel a Certain Distance with Acceleration

To determine how long it takes for the stuntman's car to travel 50 m east while accelerating at a rate of -2 m/s2, we need to use the kinematic equations of motion that relate displacement, initial velocity, acceleration, and time. Since we're given the initial velocity (vi = 20 m/s), the acceleration (a = -2 m/s2), and the displacement (d = 50 m), we can use the following equation:

d = vit + ½at2

Plugging the values into the equation, we get:

50 = 20t - (1/2)(2)t2

This simplifies to:

50 = 20t - (1)t2

Rearranging to form a quadratic equation:

t2 - 20t + 50 = 0

The above quadratic equation can be solved using the quadratic formula or factoring. Solving for t yields:

t = 5 s or t = 10 s

The negative root is discarded since time cannot be negative. Therefore, the correct answer is B. 10 s.