The acceleration of a bus is given by a_x(t)=at, where a=1.2ms^-2. a. If the bus's velocity at time t=1.0s is 5.0ms^-1, what is its velocity at time t=2.0s? b. If the bus's position at time t=1.0s is 6.0m, what is its position at time t=2.0s? c. Sketch a_x-t, v_x-t, and x-t graphs for the motion.

The acceleration of a bus is given by a_x(t)=at, where a=1.2ms^-2. a.

1.	The acceleration of a bus is given by a_x(t)=at, where a=1.2ms^-2. a. If the bus's velocity at time t=1.0s is 5.0ms^-1, what is its velocity at time t=2.0s? b. If the bus's position at time t=1.0s is 6.0m, what is its position at time t=2.0s? c. Sketch a_x-t, v_x-t, and x-t graphs for the motion.
Answer» SOLUTION :a. The VELOCITY `v_2` at time `t` `v_2=v_1+int_(t_1)^(t)atdt` `=v_1+alpha/2(t^2-t_1^2)` `=v_1-alpha/2t_1^2+alpha/2t^2` `=(5.0ms^-1)-(0.6ms^-3)(1.0s)^2+(0.6ms^-3)t^2` `=(4.40ms^-1)+(0.6ms^-3)t^2`. At `t_2=2.0s`, the velocity is `v_2=(4.40ms^-1)+(0.6ms^-3)(2.0s)^2` `=6.80ms^-1`, or `6.8ms^-1` to two significant figures. b. the POSITION `x_2` as a function of time is `x_2=x_1+int_(t_1)^tv_xdt` `=(6.0m)+int_(t_1)^t(4.40ms^-1)+(0.6ms^-3)t^(2))dt` `=(6.0m)+(4.40ms^-1)(t-t_1)+((0.6ms^-3))/(3)(t^3-t_1^3)` At `t=2.0s`, and with `t_1=1.0s`, `X=(6.0m)+(4.40ms^-1)[(2.0s)-(1.0s)]` `+(0.20ms^-3)[(2.0s)^3-(1.0s)^3]=11.8m` C.