x=5t^3-6t^2-7t meter, what is the displacement from t1=1s to t2=3s. What is the instantaneous velocityand instantaneous acceleration?

The displacement from t=1 to t=3 is the given function
f(t)'s

f(3)-f(1)=60-(-8)=68
meters

the instantaneous velocity is the derivative of x
with respect to t

in math
notation

dx/dt

dx/dt the
original equation

using the power
rule

v(t)= 15t^2-12t-7 with t measured in seconds and
velocity measured in meters/second

the instantaneous
acceleration is the derivative of the velocity(the slope of the velocity graph) with
respect to time

dx/dt

dx/dt
the velocity equation

using the power rule
again

the constant -7 becomes
0

a(t)=30t-12 measured in
m/s^2

The final answer to this
question

The displacement from t=1 to t=3 is
68m, the instantaneous velocity is
v(t)=15t^2-12t-7

the
instantaneous acceleration function is a(t)=
30t-12