Problem 2 A particles position along the xaxis is described

Problem 2: A particle’s position along the x-axis is described by x(t) = A t + B t2, where t is in seconds, x is in meters, and the constants A and B are given below. Randomized Variables A = -4.5 m/s B = 2.3 m/s2

Part (a) What is the velocity, in meters per second, of the particle at t1 = 3.0 s?

Part (b) What is the velocity, in meters per second, of the particle when it is at the origin (x = 0) at t0 > 0?

Solution

Here ,

x = A * t + B * t^2

A = -4.5 m/s

B = 2.3 m/s^2

a) as v = dx/dt

v = A + 2 * B * t

at t = 3 s

v = -4.5 + 2 * 3 * 2.3

v = 9.3 m/s

the velocity at t1 is 9.3 m/s^2

part b)

for the particle to be at origin

x = 0

-4.5 * t + 2 * 2.3 * t^2 = 0

t = 0.978 s

velocity at this time

v = -4.5 + 2 * 3 * 0.978

v = 1.4 m/s

the velocity at this time is 1.4 m/s