A body is moving with uniform acceleration it's velocity after 4s is 16m/s and after 10s is 28m/s. Calculate the distance travelled by it 12s?
v0 + 4a = 16
v0 + 10a = 28
a=2, v0=8
s(t) = s0+ 8t + t^2
Now you can figure the distance traveled during any interval.
240m
To calculate the distance traveled by the body in 12 seconds, we need to use the equations of motion.
Given:
Initial time, t1 = 4s
Initial velocity, v1 = 0 (since we are considering the body's velocity at 4s - v1 = 0)
Final time, t2 = 10s
Final velocity, v2 = 28 m/s
First, we need to find the acceleration of the body.
Using the equation of motion:
v2 = v1 + at2
Where:
v1 = initial velocity
a = acceleration
t2 = time
Substituting the given values:
28 m/s = 0 + a * 10s
Simplifying the equation:
a = 28 m/s / 10s
a = 2.8 m/s²
Now, let's find the distance traveled by the body in 12 seconds using the following equation of motion:
s = (v2² - v1²) / (2a)
Where:
s = distance traveled
Substituting the given values:
s = (28² - 0) / (2 * 2.8)
Simplifying the equation:
s = (784 - 0) / 5.6
s = 140 m
Therefore, the distance traveled by the body in 12 seconds is 140 meters.