NUMERICALS OF INSTANTANEOUS VELOCITY

Sure, here's an example of a numerical problem involving instantaneous velocity:

Problem: A car is moving along a straight line with its position given by the function x(t) = 3t^3 - 2t^2 + 4t - 1, where x is in meters and t is in seconds. Find the car's instantaneous velocity at t = 2 seconds.

Solution:

Step 1: The instantaneous velocity of an object moving along a straight line is given by the derivative of the position function with respect to time. So, we first need to find the derivative of x(t).

Step 2: Differentiate x(t) with respect to t. The derivative of x(t) = 3t^3 - 2t^2 + 4t - 1 is x'(t) = 9t^2 - 4t + 4.

Step 3: To find the instantaneous velocity at t = 2 seconds, we substitute t = 2 into the derivative function.

Step 4: x'(2) = 9(2)^2 - 4(2) + 4 = 36 - 8 + 4 = 32 m/s.

So, the car's instantaneous velocity at t = 2 seconds is 32 m/s.