Question

A particle moves along the X axis. Its position varies with time according to the function X(t) = 4t – 2t2, where X is in meters and t is in seconds.

1. Calculate the velocity of the particle V(t)
my answer was (0s,3s)????

2.) Calculate the acceleration of the particle a(t)
My answer was (-2,2s)???

3.) Calculate the velocity at t=2.5 s
dont get that one

4) Calculator the position at time t=3.5
dont get this either

thank you

Answer 1

1).Speed is the time derivative of the equation of motion

$V(t)=\frac{dx(t)}{dt}=\frac{d(4t-2t^2)}{dt}=4-4t m/s$

i.e

$V(t)=4-4t m/s$

2).acceleration is the time derivative of speed

$a(t)=\frac{dV(t)}{dt}=\frac{d(4-4t)}{dt}=-4 m/s^2$

i.e

$a(t)=-4 m/s^2$

3.) Speed at t = 2.5 s

$V(2.5)=4-4 \cdot 2.5=4-10=-6 m/s$

4) The position of the particle at time t = 3.5 s

$x(3.5)=4t-2t^2=4 \cdot 3.5-2 \cdot 3.5^2=14-24.5=-10.5 m$