#### To determine

**To sketch:** The possible graph of the distance *s* Nick has covered after *t* minutes.

#### Explanation

**Given:**

Nick starts jogging and for the first 3 minutes, runs faster and faster, then he walks for 5 minutes.

He stops for 2 minutes at a point and runs fairly quickly for 5 minutes, then walks for 4 minutes.

**Calculation:**

**First step:**

Nick starts jogging and runs faster and faster for 3 minutes.

When Nick is jogging the distance travelled is low but distance travelled

increases rapidly when Neck starts running faster and faster.

This implies that graph of distance versus time is not a linear.

It will be a bit quadratic in shape.

**Second step:**

Nick walks for 5 minutes.

So, the distance travelled increases linearly.

This implies that graph of distance versus time is linear.

**Third step:**

Nick stops an intersection for 2 minutes.

So, the distance travelled will be zero in this time interval.

This implies that graph of distance versus time is a horizontal line.

**Fourth step:**

Nick runs fairly quickly for 5 minutes.

So, the distance travelled increases linearly.

This implies that graph of distance versus time is a linear line.

**Fifth step:**

Nick walks for 4 minutes.

So, the distance travelled increases linearly.

This implies that graph of distance versus time is a linear line.

**Graph:**

Use the above information and draw distance versus time graph

as shown in Figure 1.

#### To determine

**To sketch:** The graph of dsdt

#### Explanation

**Calculation:**

**First step:**

Nick starts jogging and runs faster and faster for 3 minutes.

Since at t=0, Nick starts jogging This implies dsdt>0

As Nick runs faster and faster his speed increases linearly.

The graph will be a linear one in this interval.

**Second step:**

Nick walks for 5 minutes.

So, the speed will be constant.

This implies that graph of will be a horizontal line.

**Third step:**

Nick stops an intersection for 2 minutes.

So, the speed will be zero

This graph is the *x*-axis in this interval..

**Fourth step:**

Nick runs fairly quickly for 5 minutes.

So, the speed will be constant this time the speed is higher than the

Speed in the interval 3 to 8 minutes.

This implies that graph of will be a horizontal line.

**Fifth step:**

Nick walks for 4 minutes.

So, the speed will be constant and will be same as the speed in the interval 3 to 8 minutes.

This implies that graph of will be a horizontal line.

**Graph:**

Use the above information and draw the graph of distance versus time as shown

in Figure 2.

**Observation:**

The graph is discontinuous at points x=3,8,10,15.