#### To determine

**To find:**

The speed of the car when it has travelled 60 meters.

#### Answer

32.14 m/s

#### Explanation

**1) Concept:**

The work is calculated by using the formula W=∫x1x2fxdx

**2) Given:**

The mass of the car is 800 kg and the force is 5.7x2+1.5x N

**3) Calculation:**

Using the given information calculate the work done by the 800 kg roller coaster car with force 5.7x2+1.5x N using the formula the work done is W=∫x1x2fxdx

W=∫0605.7x2+1.5x dx

W=5.7x33+1.5x22060

W=1.96033+0.756022

W=413100 J.

Now use the exercise 31a) W=12mv22-12mv12 To find the speed of the car when it has travelled a distance 60 meters, initially, the speed was 0 so let v1=0

Therefore, the expression of W becomes

W=12mv22

413100=12·800·v22

413100=400·v22

v22=413100400

v2=32.14 m/s

**Conclusion:**

The speed of the car when it has travelled 60 meters is 32.14 m/s