Question

a man set out in his car with a velocity of 10m/s and accelerated uniformly to his destination in 1/4 minutes .If his velocity on arrival was 100m/s, how far is the destination from his house?​

Answer 1

The distance to the destination is 148,500 meters.

Step-by-step explanation:

To find the distance to the destination, we need to use the formula:

`d = (vf^2 - vi^2) / (2a)`

Where:

• d is the distance
• vf is the final velocity
• vi is the initial velocity
• a is the acceleration

In this case, the initial velocity is 10 m/s, the final velocity is 100 m/s, and the time is 1/4 minutes, which is 15 seconds.

First, we need to convert the time to seconds:

• 1 minute = 60 seconds
• 1/4 minutes = 15 seconds

Using the formula:

`d = (100^2 - 10^2) / (2 * a)`

Substituting the values:

d = (10000 - 100) / (2 * a)

Simplifying:

d = 9900 / (2 * a)

Now, we can solve for the acceleration:

15 = 1 / (2 * a)

1 / 15 = 2 * a

2a = 1 / 15

a = 1 / (15 * 2)

a = 1 / 30

Substituting the value of acceleration back into the distance formula:

d = 9900 / (2 * (1 / 30))

Simplifying:

d = 9900 / (2 / 30)

d = 9900 * (30 / 2)

d = 148500

Therefore, the distance to the destination is 148,500 meters.