A car is travelling in the velocity of 20m/s.After 30 sec it covers a distance of 1200m.calculate the accelaration of the car and final velocity of the car.
To calculate the acceleration and final velocity of the car, we can use the following kinematic equation:
\[ v_f = v_i + at \]
where:
- \( v_f \) is the final velocity of the car,
- \( v_i \) is the initial velocity of the car,
- \( a \) is the acceleration of the car,
- \( t \) is the time.
Given that the initial velocity (\( v_i \)) is 20 m/s, the time (\( t \)) is 30 seconds, and the distance traveled is 1200 meters, we can determine the final velocity and acceleration.
First, we need to find the final velocity (\( v_f \)) using the formula:
\[ v_f = v_i + at \]
Substituting the values we have:
\[ v_f = 20 \, \text{m/s} + a \times 30 \, \text{s} \]
Now, we use the formula for distance:
\[ d = v_i \times t + \frac{1}{2} a t^2 \]
Substituting the values given:
\[ 1200 \, \text{m} = 20 \, \text{m/s} \times 30 \, \text{s} + \frac{1}{2} a \times (30 \, \text{s})^2 \]
Now we solve these equations simultaneously to find the acceleration (\( a \)) and final velocity (\( v_f \)).
at time t,
s = 20t + 1/2 a t^2
so, we can find a by solving
20*30 + 1/2 a * 30^2 = 1200
a = 4/3 m/s^2
v = 20 + at = 20 + 4/3 * 30 = 60 m/s