Hi, I need some help with a homework problem invovling acceleration

• mindgame
In summary, the acceleration of the car can be calculated by finding the rate of change of velocity with time. By using the equation a=Δv/t, the acceleration was found to be 2.2225 m/s, based on the given data. The trendline of v(t) = 3.6688t + 5.6189 shows the slope of the graph and can be used to determine the gradient in the equation for acceleration.
mindgame

Homework Statement

What is the acceleration of your car?

Time Velocity[ms]
1 8.8
2 12.82
3 16.25
4 20.46
5 24.22
6 28.09
7 31.77
8 35.24
9 39.32
10 42.37
11 44.61
12 46.63
13 49.01
14 50.53
15 52.1
16 52.32
17 53.6
18 53.44
19 53.74
20 53.25

http://img87.imageshack.us/img87/8674/velocitygraphob6.jpg

The Attempt at a Solution

Last edited by a moderator:
I really just don't know where to start, is there an equation I need to use or is this much more complicated?

The definition of acceleration is the rate of change of velocity with time. What you need to do is find out how much the speed changed and in what time, then:

$$a= \frac{\Delta v}{t}$$

(53.25 - 8.8) = 44.45

a = (44.45) / 20s

a = 2.2225 m/s

Is this right?

What's with the function in the upper right edge v(t) = 3.6688 t + 5.6189 ?

That's just the slope of the trendline for the increasing part of the graph. He told us in class we had to show it.

Ok, so from above $$a= \frac{\Delta v}{t}$$ , or to put it another way, a is the gradient of the graph of v against t. Given your trendline, in the form y=mx+c, how can you read off the gradient?

What is acceleration?

Acceleration is a measure of the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. It is calculated by dividing the change in an object's velocity by the time it takes for that change to occur.

How is acceleration related to velocity?

Acceleration and velocity are closely related, as acceleration is the rate of change of velocity. This means that when an object's acceleration changes, its velocity will also change. For example, if an object is accelerating in a straight line, its velocity will either increase or decrease depending on the direction of the acceleration.

What is the difference between average and instantaneous acceleration?

Average acceleration is the change in an object's velocity over a specific time interval, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated by dividing the change in velocity by the time interval, while instantaneous acceleration can be found by taking the derivative of the velocity with respect to time.

What factors can affect acceleration?

Acceleration can be affected by a variety of factors, including the force applied to an object, the mass of the object, and any external forces acting on the object (such as friction or air resistance). Additionally, the direction of acceleration can also be influenced by the direction of the applied force.

How can acceleration be represented graphically?

Acceleration can be represented on a graph by plotting an object's velocity over time. The slope of the line on the graph represents the object's acceleration, with a steeper slope indicating a higher acceleration. The area under the curve on a velocity-time graph also represents the object's change in velocity, and therefore, its acceleration.