An object moves in a straight
line and the distance v in meters
moved in t seconds is given by v
= t4 — 3t + 2. What is the speed
at t= 3 secs?
A. 117m/s
B. 105m/s
C. 122m/s
D. 187m/s
To find the speed at t = 3 seconds, we need to differentiate the equation v = t^4 - 3t + 2 with respect to time t.
The derivative of v with respect to t is dv/dt = 4t^3 - 3.
To find the speed, we need to evaluate dv/dt at t = 3 seconds.
Substituting t = 3 into dv/dt, we get dv/dt = 4(3)^3 - 3 = 108 - 3 = 105 m/s.
Therefore, the speed at t = 3 seconds is 105 m/s.
The correct answer is B. 105m/s
To find the speed at t=3 seconds, we need to find the derivative of the distance equation v = t^4 - 3t + 2 with respect to t.
Let's find the derivative:
dv/dt = 4t^3 - 3
Now, substitute t=3 into the derivative equation:
dv/dt = 4(3)^3 - 3
dv/dt = 4(27) - 3
dv/dt = 108 - 3
dv/dt = 105
Therefore, the speed at t=3 seconds is 105 m/s.
The correct answer is B. 105m/s.