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

Answer:

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

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

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

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

Answer 2

Answer:

option (c)

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.