Question

A shopping cart is rolling down a ramp with an initial velocity of + 1.0 m s +1.0 s m ​ plus, 1, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction at t = 0 seconds t=0secondst, equals, 0, start text, s, e, c, o, n, d, s, end text and a constant acceleration of 3.0 m s 2 3.0 s 2 m ​ 3, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. What can be said about the shopping cart’s direction of travel and speed at t = 2 seconds t=2secondst, equals, 2, start text, s, e, c, o, n, d, s, end text? Choose 1 answer:

Answer 1

The kinematic relations allow finding that the answers for the velocity and the position of the car in a time of 2 s. are:

• The velocity is v = 7 m / s

• The position is x = 8 m

 

Kinematics studies the movement of bodies giving relationships between the position, velocity and acceleration of the body

They indicate that the initial velocity is v₀ = 1 m/s, that the car has an acceleration of a = 3 m/s² and asks about the position and velocity after a time of t = 2s

Let's used the kinematics relation

                 v = v₀ + a t

                 v = 1 + 3 2

                 v = 7 m / s

We look for the position

                  x = v₀ t + ½ a t²

                 x = 1 2 + ½ 3 2²

                 x = 8m

In conclusion, using the kinematics relations we can find the answers for the speed and the position of the car in a time of 2 S. They are

• The velocity is v = 7 m / s

• The position is x = 8m

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