Answer to Question #301265 in Physics for Lei

Question

Evaluate:

HORIZONTAL MOTION

1. The motion of a particle along the x -axis is described by the equation

m v = (3 s2) t + (0.5 m) t2 s2

where x is in meters, and t is in seconds. Determine the following:

a. Position of the particle 3 seconds after starting

b. Displacement from 2 sec to 5 sec c. Average velocity during first 5 seconds d. Velocity at t = 4secs

UARM:

e. Average acceleration during the second 3 seconds

f. Acceleration at t = 5 secs g. Time the particle moves at 20m/s

h. The acceleration and velocity at start of motion 1. A car is moving at uniform acceleration. Its velocity

Answer 1

$x(t)= 3t +0.5t^2$

a. Position of the particle 3 seconds after starting

$$x(3)= 3*3 +0.5*3^2=13.5\:\rm m$$

b. Displacement from 2 sec to 5 sec

$$x(5)-x(2)=(3*5+0.5*5^2)\\ -(2*5+0.5*2^2)=15.5\:\rm m$$

c. Average velocity during first 5 seconds

$$x(5)= 3*5 +0.5*5^2=27.5\:\rm m$$

$$v_{\rm ave}=\frac{x(5)}{t}=\frac{27.5}{5}=5.5\:\rm m/s$$

d. Velocity at t = 4sec

$$v=x'=3+t$$

$$v(4)=3+4=12\:\rm m/s$$