When S is measured in meters and t in seconds, find the velocity at time t =2 of the motion S = t2 – 3t2A.-4B.27C.3D.-3
Question
When S is measured in meters and t in seconds, find the velocity at time t = 2 of the motion
Options:
A. -4
B. 27
C. 3
D. -3
Solution
To find the velocity at time t = 2, we need to differentiate the equation S = t^2 - 3t^2 with respect to time.
Step 1: Differentiate the equation S = t^2 - 3t^2 with respect to time t.
dS/dt = d(t^2 - 3t^2)/dt
Step 2: Apply the power rule of differentiation.
dS/dt = 2t - 6t
Step 3: Substitute t = 2 into the derivative equation to find the velocity at time t = 2.
v = 2(2) - 6(2)
Step 4: Simplify the equation.
v = 4 - 12
v = -8
Therefore, the velocity at time t = 2 is -8.
The correct answer is D. -8.
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