How Do You Calculate Acceleration and Velocity in Physics Problems?

[jkt]

Homework Statement

I'm trying to solve the following problem to help my son with his homework...

Suppose you build a motor car that travels across a table top a distance of 1.5 meters in 1.2 seconds. The table is 0.8 m tall. The mass of the car is 300 grams. Ignore friction, air resistance.
1) If we assume that its acceleration is uniform, what is the acceleration of the car while rolling on the table? The correct answer is 2.1 m/s/s...but i don't understand how that answer was arrived at.

2) What would be the velocity of the car after it has accelerated across the table top for the distance of 1 meter? The correct answer 2.5 m/s...but once again, I don't understand it. Any help for the weary mom?

Homework Equations

speed = distance/time

The Attempt at a Solution

1.5/1.2

 

[neutrino]

speed = distance/time

That would apply if the speed was same during the travel. speed/time, in this problem, would only result in the average speed.

Given distance and time, which of the kinematic equations would you use to find the acceleration?

(I guess the you've to assume that the car starts from rest)

 

[m2003]

= 1.25 m/s

The speed of the car is 1.25 m/s.

To find the acceleration, we use the formula acceleration = (final velocity - initial velocity)/time.

The final velocity is the speed of the car, which is 1.25 m/s. The initial velocity is 0 m/s since the car starts from rest. The time is 1.2 seconds.

Therefore, acceleration = (1.25 m/s - 0 m/s)/1.2 s = 1.25/1.2 = 1.04 m/s/s.

This is not the correct answer of 2.1 m/s/s, but it is close. This is because we have not taken into account the fact that the car is rolling on a table that is 0.8 m tall. This means that the car is not only moving horizontally, but also vertically. In order to find the correct answer, we need to use the Pythagorean theorem to find the total distance traveled by the car.

The distance traveled by the car is the hypotenuse of a right triangle with sides of 1.5 m and 0.8 m. Using the Pythagorean theorem, we get:

Distance = √(1.5^2 + 0.8^2) = √(2.25 + 0.64) = √2.89 = 1.7 m

Now we can use the formula speed = distance/time to find the speed of the car:

Speed = 1.7 m/1.2 s = 1.42 m/s

The acceleration of the car is now:

Acceleration = (final velocity - initial velocity)/time = (1.42 m/s - 0 m/s)/1.2 s = 1.42/1.2 = 1.18 m/s/s

This is still not the correct answer, but it is closer. The reason for this is that we have not taken into account the mass of the car. In order to find the correct answer, we need to use the formula F=ma, where F is the force, m is the mass, and a is the acceleration.

We know that the car has a mass of 300 grams, which is equal to 0.3 kg. We also know that the force acting on the car is its weight, which is equal to mg, where g is