MC$422-$Dynamics in Class Assignment # $1$

A car is at position $"O"$ with a speed of $50f\frac{t}{s}$ when it begins to brake. The speed decreases

at a constant rate of $1f\frac{t}{s^2}.$ The car continues to brake at this rate as it travels from $O$ to $B.$

Assume that the section $O-A$ is a straight path and $A-B$ is a $\frac{1}{4}-$circular path.

$($a$)$ What is the speed of the car when it enters the curve at A$?$

$($b$)$ What are the normal and tangential components of acceleration of the car just after it

enters the curve at $A?$

$($c$)$ What are the magnitude and direction of the car's acceleration just after it enters the

curve at $A?$

$($d$)$ Calculate the total distance the car travels from $O$ to $B.($circumference of a

circle $=2r).$

$($e$)$ What is the speed of the car at $B?$

$($f$)$ What are the normal and tangential components of acceleration of the car just before

it exits the curve at $B?$

$($g$)$ What are the magnitude and direction of the car's acceleration just before it exits the

curve at $B?$

$($h$)$ How long in seconds does it take for the car to travel from $O$ to $B?$

Kinematic equations:

For constant $a=a_{}$

$v=v_0+a_{c}t$

$s=s_0+v_{0}t+\frac{1}{2}{a}_c{t}^2$

$v^2-v_0^2=2a_c(s-s_0)$

Curvilinear motion:

$a_t=\frac{dv}{dt},a_n=\frac{v^2}{},|vec(a)|=\sqrt[\phantom{2}]{a_t^2+a_n^2}$