Question

Suppose that a car traveling with constant speed to the west takes a 90° left turn toward south. Which of the following statements about its acceleration in the midpoint of the turn is correct? Flag question Select one: a. The acceleration is toward the north-west. b. The acceleration is toward south. c. The acceleration is toward the south-east. O d. Since the speed s constant the acceleration is zero

Answer 1

option (c)

Step-by-step explanation:

Let the speed of car is v.

It is travelling along the west direction. So write the initial velocity of the car in vector form.

`\overrightarrow{v_(1)}=-v\widehat{i}`

Now it takes a left turn at 90°, write the final velocity in vector form.

`\overrightarrow{v_(2)}=-v\widehat{j}`

Acceleration is given by the rate of change of velocity, so the direction of acceleration is same as the direction of change in velocity.

`\overrightarrow{a}=\frac{\overrightarrow{v_(2)}-\overrightarrow{v_(1)}}{t}`

`\overrightarrow{a}=\frac{-v\widehat{j}+v\widehat{i}}{t}=\frac{v\widehat{i}-v\widehat{j}}{t}`

The direction of the acceleration is towards south east.

Answer 2

The correct answer is option 'c': The acceleration is towards south east.

Step-by-step explanation:

The initial velocity vector of the car is
`v_(i)=-v\widehat{i}`

The final velocity vector of the car is
`v_(f)=-v\widehat{j}`

Thus by definition of acceleration we have

`\overrightarrow{a}=\frac{\overrightarrow{v_(f)}-\overrightarrow{v_(i)}}{t_(f)-t_(i)}\\\\\therefore \overrightarrow{a}=\frac{-v\widehat{j}+v\widehat{i}}{t_(f)-t_(i)}\\\\\overrightarrow{a}=(1)/(\Delta t)(v\widehat{i}-v\widehat{j})`

From the direction of the acceleration vector we conclude that the direction is towards south east.