Question

A car with a velocity of 10 m/s is accelerated uniformly at the rate of 2 m/s². How long does it take to travel for 200 m?

A) 10 m/s
B) 15 m/s
C) 20 m/s
D) 30 m/s

Answer 1

Note that the units of the answer options are all m/s, not just seconds. m/s is velocity. If these units were all meant to be just seconds, the answer is

A) 10 seconds

Step-by-step explanation:

The equation for an object that is accelerating is

d = vi*t + (1/2)*a*t^2,

where vi is the initial velocity, a is acceleration (in m/s^2), and t is time in seconds.

vi = 10 m/s

a = 2 m/s^2

d = 200 m

200m = (10 m/s)*t + (1/2)*(2 m/s^2)*t^2

200m = (10 m/s)*t + (1 m/s^2)*t^2

(1 m/s^2)*t^2 + (10 m/s)*t - 200m = 0

This is in the form of 1x^2 + 10x - 200 = 0

Solve using the quadratic equation.

x = 10 and x = -20

We can drop the - 20 and just use 10

This means that t = 10 seconds

Lets try t=10 s in the equation to see if we get 200 m.

d = vi*t + (1/2)*a*t^2

d = (10m/s)*(10s) + (1/2)*(2m/s^2)*(10)^2

d = (100m)+ (100m) = 200 meters It checks OK.