Physics 2000 JAMB Past Questions - Question 8: The velocity v of a particle in a time t is given by the equation v = 10 + 2t² Find the instantaneous acceleration after 5 seconds.

Correct Answer

C

Explanation

To find the instantaneous acceleration after 5 seconds, you'll need to take the derivative of the velocity equation with respect to time (t) to find the acceleration function and then evaluate it at t = 5 seconds.To find the instantaneous acceleration after 5 seconds, we need to differentiate the velocity equation with respect to time (t) to obtain the acceleration equation.

Given:
v = 10 + 2t²

Differentiating both sides of the equation with respect to time (t), we get:

dv/dt = d/dt (10 + 2t²)

The derivative of a constant term (10) with respect to time is zero, and the derivative of 2t² with respect to time is 4t. Therefore, the equation becomes:

dv/dt = 4t

Now, we can substitute the value of t = 5 seconds into the acceleration equation:

a = dv/dt (at t = 5)

a = 4(5)
a = 20

Therefore, the instantaneous acceleration after 5 seconds is 20 units.

Given the velocity equation:
v = 10 + 2t²

First, take the derivative of v with respect to t to find the acceleration (a):
a = dv/dt = d/dt (10 + 2t²)

Now, differentiate each term:
da/dt = d/dt (10) + d/dt (2t²)

The derivative of a constant (10) is zero, and for 2t², you can use the power rule for differentiation, which states that d/dt (t^n) = nt^(n-1). In this case, n = 2:

da/dt = 0 + 2 * 2t^(2-1) = 4t

So, the acceleration function is:
a = 4t

Now, you want to find the instantaneous acceleration after 5 seconds, so plug in t = 5 into the acceleration equation:

a(5) = 4 * 5
a(5) = 20 m/s²

The instantaneous acceleration of the particle after 5 seconds is 20 m/s².