Question

(2) what does it mean when an object has a westward velocity and an eastward acceleration?
(3) describe the three ways that an object can accelerate.
(4) a race car starts from rest and uniformly accelerates to the left until it reaches a velocity of 35 m/s. if this change in velocity occurs over time of 3.5 seconds, what is the average acceleration of the race car?

Explanation:

Step1: Recall velocity - acceleration relationship

Velocity and acceleration are vector - quantities. When an object has a westward velocity and an eastward acceleration, the acceleration is in the opposite direction of the velocity. This means the object is slowing down (decelerating) as the force causing the eastward acceleration is acting against the westward - moving object.

Step2: List acceleration ways

An object can accelerate in three ways: 1) Change in speed: speeding up or slowing down. For example, a car accelerating from 30 mph to 60 mph or braking from 60 mph to 30 mph. 2) Change in direction: moving in a curved path. For instance, a car going around a circular track at a constant speed is still accelerating because its direction is changing. 3) Change in both speed and direction: like a car accelerating while turning a corner.

Step3: Use acceleration formula

The formula for average acceleration is $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time. The initial velocity $v_0 = 0$ m/s, the final velocity $v = 35$ m/s, and $\Delta t=3.5$ s. Then $\Delta v=v - v_0=35 - 0=35$ m/s. So, $a=\frac{35}{3.5}=10$ m/s².

Answer:

(2) The object is decelerating as the acceleration is in the opposite direction of its velocity.
(3) An object can accelerate by changing its speed, changing its direction, or changing both its speed and direction.
(4) 10 m/s²