an object moves in a straight line and the distance v in meters moved in t seconds is given by v= t^4-3t+2. what is the speed at t= 3 seconds
To find the speed at t = 3 seconds, we need to calculate the derivative of the distance equation with respect to time and then substitute t = 3 into the derivative.
Let's find the derivative of v(t) = t^4 - 3t + 2 first.
Taking the derivative of each term, we have:
v'(t) = 4t^3 - 3
Now, let's substitute t = 3 into the derivative:
v'(3) = 4(3)^3 - 3
= 4(27) - 3
= 108 - 3
= 105
Therefore, the speed at t = 3 seconds is 105 meters per second.
To find the speed at t = 3 seconds, we need to differentiate the distance function with respect to time, t, to obtain the velocity function. The velocity function will give us the speed at any given time.
Given that v = t^4 - 3t + 2, we can differentiate it with respect to t:
dv/dt = 4t^3 - 3.
Now, let's substitute t = 3 into the velocity function:
v' = 4(3)^3 - 3
= 4(27) - 3
= 108 - 3
= 105.
Therefore, the speed at t = 3 seconds is 105 meters per second.