Question

A particle has a constant acceleration of 6.0 m/s². (a) If its initial velocity is 2.0 m/s, at what time is its displacement 5.0 m? (b) What is its velocity at that time?

a) (a) 1.0 s, (b) 32.0 m/s
b) (a) 5.0 s, (b) 10.0 m/s
c) (a) 10.0 s, (b) 2.0 m/s
d) (a) 4.0 s, (b) 12.0 m/s

Answer 1

The particle's displacement is 5.0 m at time t = 1.0s, and its velocity at that time is 8.0 m/s.

Step-by-step explanation:

In order to answer the questions, we can use the equations of motion.

(a) To find the time when the displacement is 5.0 m, we can use the equation:

Δx = ut + 0.5at²

Where Δx is the displacement, u is the initial velocity, a is the acceleration, and t is the time.

Substituting the given values, we have:

5.0 = 2.0t + 0.5(6.0)t²

Simplifying the equation gives us a quadratic equation, which can be solved to find t = 1.0 s or t = 2.0 s. However, since the initial velocity is positive, we can discard the negative value and conclude that the time when the displacement is 5.0 m is 1.0 s.

(b) To find the velocity at that time, we can use the equation:

v = u + at

Substituting the given values, we have:

v = 2.0 + (6.0)(1.0)

Simplifying the equation gives us v = 8.0 m/s.