A car is projected directly up an incline and its location from its start point is given by the formula
s = 9t - 5t2. Determine its initial velocity and initial acceleration.
initial velocity in m/s =
initial acceleration in m/s2 =
My Answer
s'=9-10t
initial velocity in m/s = 9
S"= -10
initial acceleration in m/s2 = -10
Can you please confirm this..
thanks!
To determine the initial velocity and initial acceleration, we need to observe the given formula and its derivatives.
The given equation is s = 9t - 5t^2, where s represents the location at time t.
To find the initial velocity, we need to determine the derivative of the position function with respect to time (s').
Taking the derivative of s = 9t - 5t^2 with respect to t, we get:
s' = 9 - 10t.
Therefore, the initial velocity (v0) is given by substituting t = 0 into s':
v0 = s'(0) = 9 - 10(0) = 9 m/s.
So, the initial velocity is 9 m/s.
To find the initial acceleration, we need to find the derivative of s' with respect to time (s'').
Taking the derivative of s' = 9 - 10t with respect to t, we get:
s'' = -10.
Therefore, the initial acceleration (a0) is given by substituting t = 0 into s'':
a0 = s''(0) = -10 m/s^2.
So, the initial acceleration is -10 m/s^2.
Hence, your answer is correct. The initial velocity is 9 m/s, and the initial acceleration is -10 m/s^2.