If the displacement of an object is given in SI units by Δx = −5t + t ²,at t = 2 s its velocity and acceleration are,respectively: (Hint: Use dimensional analysis along with the equations for motion with constant acceleration. ) A) positive,positive. B) positive,negative. C) negative,negative. D) negative,positive.

Question

Quizplus · Accepted Answer

We can use the equations for motion with constant acceleration:
v = u + at
s = ut + 0.5 at^2
where u is the initial velocity, v is the final velocity, a is the acceleration, and s is the displacement.

Since the given displacement equation is Δx = −5t + t^2, we can find the velocity by differentiating with respect to time:
v = d(Δx)/dt = -5 + 2t
At t = 2 s, v = -5 + 2(2) = -1 m/s, which is negative. Therefore, the answer cannot be A or B.

To find the acceleration, we differentiate the velocity with respect to time:
a = d(v)/dt = 2 m/s^2
Since a is positive, the answer cannot be C, leaving D as the only choice. Therefore, the velocity at t= 2s is negative and the acceleration is positive.

If the Displacement of an Object Is Given in SI