Question

a car is moving at a speed of 40 km/h. it hits the brakes and slows down at a rate of (-10 km/h) for 3 seconds. what is its final velocity? for 5 seconds. a ball rolls down a hill, speeding up at a rate of 7 m/s². what’s the ball’s final velocity?

Explanation:

Step1: Identify the initial - velocity, acceleration, and time for the car

Initial velocity of the car $u = 40$ km/h, acceleration $a=- 10$ km/h, and time $t = 3$ s. First, convert the time from seconds to hours. Since $1$ hour = $3600$ s, $t=\frac{3}{3600}=\frac{1}{1200}$ h.

Step2: Use the velocity - time formula $v = u+at$ for the car

$v = 40+( - 10)\times\frac{1}{1200}=40-\frac{1}{120}=\frac{4800 - 1}{120}=\frac{4799}{120}\approx39.99$ km/h

Step3: Identify the initial - velocity, acceleration, and time for the ball

Assume the initial velocity of the ball $u = 0$ m/s (starts from rest), acceleration $a = 7$ m/s², and time $t = 5$ s.

Step4: Use the velocity - time formula $v = u+at$ for the ball

$v=0 + 7\times5=35$ m/s

Answer:

The final velocity of the car is approximately $39.99$ km/h and the final velocity of the ball is $35$ m/s.