Calculus of a Single Variable

Acceleration At the instant the traffic light turns green, a car that has been waiting at an intersection starts with a constant acceleration of 6 feet per second per second. At the same instant, a truck traveling with a constant velocity of 30 feet per second passes the car.

(a) How far beyond its starting point will the car pass the truck?

(b) How fast will the car be traveling when it passes the truck?

Calculus of a Single Variable

Deceleration A car traveling at 45 miles per hour is brought to a stop, at constant deceleration, 132 feet from where the brakes are applied.

(a) How far has the car moved when its speed has been reduced to 30 miles per hour?

(b) How far has the car moved when its speed has been reduced to 15 miles per hour?

(c) Draw the real number line from 0 to $132 .$ Plot the points found in parts (a) and (b). What can you conclude?

Calculus of a Single Variable

Acceleration The maker of an automobile advertises that it takes 13 seconds to accelerate from 25 kilometers per hour to 80 kilometers per hour. Assume the acceleration is constant.

(a) Find the acceleration in meters per second per seconds.

(b) Find the distance the car travels during the 13 seconds.

Calculus of a Single Variable

A particle, initially at rest, moves along the $x$ -axis such thatits acceleration at time $t>0$ is given by $a(t)=\cos t .$ At time $t=0,$ its position is $x=3$

(a) Find the velocity and position functions for the particle.

(b) Find the values of $t$ for which the particle is at rest.