Answer to Question #137799 in Physics for Gigma Hill

Question

A car initially at rest accelerates at 10 m/s2. The car’s speed after it has traveled 25 meters is most nearly:

A. 0 m/s
B. 25 m/s
C. 22 m/s
D. 10 m/s

A driver sees a dog run out into the street. If they are traveling at 27 m/s, and the brakes slow them down at a rate of -4 m/s^2, how far will the car travel after 2 seconds?

A. 46 m
B. 8 m
C. 54 m
D. 62 m

Consider a graph of motion (position-time graph) representing the equation y = 10x, with the x-axis being time (sec) and the y-axis being distance (m). What is the Velocity of the object?

A. 10 m/s
B. 0 m/s
C. 15 m/s
D. 20 m/s
E. 5 m/s

Answer 1

A car initially at rest accelerates at 10 m/s². The car’s speed after it has traveled 25 meters is

$$v_f=\sqrt{2ad}=\sqrt{2\cdot10\cdot25}=22.4\text{ m/s}.$$

A driver sees a dog run out into the street. If they are traveling at 27 m/s, and the brakes slow them down at a rate of -4 m/s^2, after 2 seconds the car will travel a distance of

$$d=v_it+\frac{at^2}{2}=27\cdot2+\frac{-4\cdot2^2}{2}=46\text{ m}$$

Consider a graph of motion (position-time graph) representing the equation y = 10x, with the x-axis being time (sec) and the y-axis being distance (m). What is the Velocity of the object?

The velocity is 10 m/s because

$$d=vt,\\ y=10x,\\ y=d,x=t.$$