# Linear Motion at Constant Acceleration Problem

• euphoriae
In summary, the conversation discusses a cyclist starting at the top of a slope with an initial velocity of 3.00m/s and reaching the bottom of the slope in 5 seconds, traveling 50.0m. The task is to find the velocity and acceleration at the bottom of the incline, assuming constant acceleration. The equation used is \Deltax= V0t + .5at2, and after correcting a mistake in the calculation, the correct acceleration is found to be 2.80m/s2, which matches the book's answer.
euphoriae

## Homework Statement

A cyclist starts at the top of a straight slope with an initial velocity of 3.00m/s. Five seconds later, she is at the bottom of the incline, having traveled 50.0m. Find her velocity at the bottom of the hill and her acceleration, assuming it to be constant.

## Homework Equations

$$\Delta$$x= V0 + .5at2

## The Attempt at a Solution

I tried to find the acceleration first.

I got:

a= (2*[deltaX - V-initia]l)/ T2

a= [2(50-3)]/25
I keep getting 3.76 as the acceleration but the books answer is 2.80m/s2

euphoriae said:

## Homework Statement

A cyclist starts at the top of a straight slope with an initial velocity of 3.00m/s. Five seconds later, she is at the bottom of the incline, having traveled 50.0m. Find her velocity at the bottom of the hill and her acceleration, assuming it to be constant.

## Homework Equations

$$\Delta$$x= V0t + .5at2

I keep getting 3.76 as the acceleration but the books answer is 2.80m/s2

You forgot the t after V_o! See above in red.

wow I feel dumb, thanks for the help! spent like 30mins trying to figure out what I did wrong =p

## 1. What is linear motion at constant acceleration?

Linear motion at constant acceleration is a type of motion in which an object moves in a straight line and its velocity changes at a constant rate. This means that the object's acceleration remains constant throughout its motion.

## 2. How is constant acceleration calculated?

Constant acceleration can be calculated by dividing the change in velocity by the change in time, or by using the formula a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 3. What is the difference between velocity and acceleration?

Velocity is the rate of change of an object's displacement over time, while acceleration is the rate of change of an object's velocity over time. In other words, velocity measures how fast an object is moving, while acceleration measures how quickly its velocity is changing.

## 4. How does constant acceleration affect an object's motion?

Constant acceleration causes an object to move with a continuously increasing or decreasing velocity, depending on the direction of the acceleration. This can result in a linear, curved, or parabolic motion, depending on the initial velocity and the direction and magnitude of the acceleration.

## 5. What are some real-life examples of linear motion at constant acceleration?

Some real-life examples of linear motion at constant acceleration include a freely falling object, a car accelerating or decelerating on a straight road, and a rocket launching into space.

• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Mechanics
Replies
1
Views
940
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
17
Views
7K
• Introductory Physics Homework Help
Replies
4
Views
3K