A car is moving at 3m/s when it begins to be accelerated at 5.5 m/s^2. How long does the car take to reach a speed of 5 m/s? How far does it go during this period?

Question

A car is moving at 3m/s when it begins to be accelerated at 5.5 m/s^2. How long does the car take to reach a speed of 5 m/s? How far does it go during this period? -> the distance traveled during that time is?

Answer 1

This is a very typical Kinematics problem: a linear motion with a constant acceleration.

At any time t, the motion is determined by the 3-variable set (x,v,t). If any one of them is known, the other two can be calculated with kinematics equations. In this case, v is given as 5m/s, then x and t can be calculated using the equations shown by Arturo.

Other variations of this type of problems could be giving you how far it went (x) or how long it took (t), then asking you to calculate the other two variables, respectively.

Answer 2

v = v₀ + at ⇒

t = (v - v₀) / a

v₀ = 3 m/s

v = 5 m/s

a = 5.5 m/s²

Plug in these numbers and get t in seconds. To find the distance x, use the kinematic relation

v² - v₀² = 2ax ⇒

x = (v² - v₀²) / (2a)

You have all the numbers in compatible units. Plug them in and get x in meters.