A body moves along a straight line from rest with an acceleration of 2m/s². Calculate the time taken by it to cover a distance of 100m.
distance=vi*time+1/2 a t^2
100=0+1/2 * 2*t^2
calculate time t.
To calculate the time taken by the body to cover a distance of 100m, we can use the following kinematic equation:
\[ s = ut + \frac{1}{2}at^2 \]
where:
- \( s \) is the distance covered (100m),
- \( u \) is the initial velocity (0 m/s, as it starts from rest),
- \( a \) is the acceleration (2 m/s²),
- \( t \) is the time taken.
Substituting the given values into the equation, we get:
\[ 100 = 0 \cdot t + \frac{1}{2} \cdot 2 \cdot t^2 \]
Simplifying the equation further:
\[ 100 = t^2 \]
Taking the square root of both sides, we find:
\[ t = \sqrt{100} \]
\[ t = 10 \]
Therefore, the time taken by the body to cover a distance of 100m is 10 seconds.
To calculate the time taken by the body to cover a distance of 100m, we can use the basic kinematic equation:
\[ s = ut + \frac{1}{2}at^2 \]
Where:
- s is the distance covered (in this case, 100m)
- u is the initial velocity (0m/s, since the body starts from rest)
- a is the acceleration (2m/s²)
- t is the time
Rearranging the equation to solve for time (t), we have:
\[ t = \sqrt{\frac{2s}{a}} \]
Substituting the given values into the equation, we get:
\[ t = \sqrt{\frac{2 \times 100}{2}} = \sqrt{\frac{200}{2}} = \sqrt{100} = 10 \]
Therefore, the time taken by the body to cover a distance of 100m is 10 seconds.