A car travels east at 96 km / h for 1.0 h. It then travels 30.0^∘ east of north at 128 km / h fo

A car travels east at 96 km / h for 1.0 h. It then travels...

A car travels east at $96 \mathrm{km} / \mathrm{h}$ for $1.0 \mathrm{h}$. It then travels $30.0^{\circ}$ east of north at $128 \mathrm{km} / \mathrm{h}$ for $1.0 \mathrm{h} .$ (a) What is the average speed for the trip? (b) What is the average velocity for the trip?

Key Concepts

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. It is a scalar quantity and does not take into account the direction of travel. In problems involving multiple segments of motion, the distances from each segment are summed to obtain the total distance before dividing by the total time.

Average Velocity

Average velocity is the displacement divided by the total time of the trip, making it a vector quantity. Displacement is the net change in position from the starting point to the final position, and its calculation requires both magnitude and direction. Therefore, average velocity gives insight into the overall change in position and its orientation.

Displacement

Displacement refers to the straight-line distance from the initial position to the final position, including direction. Unlike the total distance traveled, displacement considers only where the journey started and ended, making it essential for calculating average velocity in vector motion problems.

Vector Resolution

Vector resolution involves decomposing a vector into its horizontal and vertical components. This process is essential in problems where motion occurs at an angle, as it allows for the separate analysis of the movement along each axis. By resolving vectors into components, one can accurately calculate net displacement and subsequently the average velocity.

Transcript

00:01 According to the given problem, a car is moving at various speeds for the various segments of the distances covered by it.

00:12 So to show the distances traveled by it, first of all, we draw the directions, north, south, east, and west.

00:33 Like this.

00:35 Suppose the car starts moving from the origin o.

00:40 Initially, the car is moving at a speed of 96 km per hour due east and it moves for one hour.

00:54 So this is the displacement of the car from o to b due east.

01:09 So the distance covered o b will be given by speed into time.

01:19 It's a speed was 96 km per hour and the time given is one hour.

01:29 So the distance ob will be 96 kilometer.

01:38 After that the car turns and it starts moving in a direction which is at an angle of 30 degree east of north from north towards east like this at an angle of 30 degree so if the angle is 30 degree from east sorry from north the angle is 30 degree so the angle from east will be 60 degree this distance is supposed b c.

02:24 So the distance covered from v to c will be again given by speed into time.

02:36 This time the speed is 128 km per hour and the time again is 1 .1.

02:49 So the distance is 128 kilometer here this distance.

02:55 So i can take the components of this distance.

03:10 This was 96 km.

03:14 This is 128 kilometer at an angle of 60 degree...

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