Question

A car accelerates uniformly in a straight line with acceleration 10m/s 2 and travels 150m in a time interval of 5s. How far will it travel in the next 5s?​

Answer 1

To find the distance that will be traveled by a car in the next 5 seconds after it has been uniformly accelerating, calculate the velocity of the car after the first interval, use this as the initial velocity for the next interval, and then apply the equation of motion. The car will travel 375 meters in the next 5 seconds.

Step-by-step explanation:

The student is asking about the displacement of a car that accelerates uniformly in a straight line. To calculate the distance traveled by the car in the next 5 seconds, we can use the equation of motion s = ut + ½at² where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time. Since the car has already traveled for 5 seconds, we need to determine the velocity of the car at 5 seconds using the formula v = u + at, and then use this velocity as the initial velocity for calculating the distance covered in the next 5 seconds.

First, find the initial velocity at the end of the first 5 seconds:

v = u + at

Assuming the initial velocity is zero, the velocity after 5 seconds is:

v = 0 + (10 m/s² × 5 s) = 50 m/s

Now use this velocity to calculate the distance in the next 5 seconds:

s = ut + ½at²

Substituting u = 50 m/s, a = 10 m/s², and t = 5 s:

s = (50 m/s × 5 s) + (½ × 10 m/s² × 5 s²) = 250 m + 125 m = 375 m

Therefore, the car will travel 375 meters in the next 5 seconds.

Answer 2

Step-by-step explanation:

Given:

Acceleration of car = 10 m/s

Distance travelled in 5 sec = 150 m

To find:

Distance travelled in the next 5 seconds

Concept:

There are 2 ways to app this kind of questions .

Either , we can find the total distance travelled in 10 seconds and then subtract 150 m from it.

Whereas , you can find out the final velocity at the end of the 5th seconds. Using equation of motion, then get the distance travelled in next 5 seconds.

Calculation:

v² = u² + 2as

=> ( u + at)² = u² + 2as

=> u² + 2uat + a²t² = u² + 2as

=> 2uat + (at)² = 2as

=> 2u (10)(5) + (10 × 5)² = 2 (10)(150)

=> 100u = 3000 - 2500

=> 100u = 500

=> u = 5 m/s

Distance travelled in 10 seconds :

s = ut + ½at²

=> s = (5 × 10) + ½(10)(10)²

=> s = 50 + 500

=> s = 550 m

Distance travelled in the 2nd half will be :

d = 550 - 150

=> d = 400 m

So final answer is :