The velocity v of a particle in a time to is given by the equation v=10+2t^2 . Find the instantaneous acceleration after 5seconds
To find the instantaneous acceleration, we need to take the derivative of the velocity equation with respect to time.
Taking the derivative of v=10+2t^2 with respect to time t, we get:
a = d/dt(10+2t^2)
= 0 + 4t
= 4t
To find the instantaneous acceleration after 5 seconds, we substitute t=5 into the acceleration equation:
a = 4(5)
= 20
Therefore, the instantaneous acceleration after 5 seconds is 20 m/s^2.
To find the instantaneous acceleration, we need to take the derivative of the velocity equation with respect to time.
Let's differentiate the equation v = 10 + 2t^2:
dv/dt = d(10 + 2t^2)/dt
Since the derivative of a constant is 0, the term 10 disappears:
dv/dt = 0 + d(2t^2)/dt
Applying the power rule of differentiation, we get:
dv/dt = 0 + 2 * d(t^2)/dt
To differentiate t^2, we use the power rule again:
dv/dt = 2 * 2t^(2-1)
Simplifying the exponent, we have:
dv/dt = 4t
Now we can find the instantaneous acceleration by plugging in the value t = 5 seconds:
a = dv/dt (at t=5)
a = 4(5)
a = 20 meters per second squared
Therefore, the instantaneous acceleration after 5 seconds is 20 m/s^2.