Question

What will be its speed after 100 seconds if it starts from rest and moves through 1 km in 100 seconds with uniform acceleration?

Answer 1

To determine the speed after 100 seconds for an object that starts from rest and moves through 1 km in 100 seconds with uniform acceleration, we can use the equations of motion.

First, let's convert the distance from kilometers to meters since the unit of speed will be in meters per second (m/s).

1 km = 1000 meters

So, the distance covered is 1000 meters, and the time taken is 100 seconds.

We can use the following equation of motion:

$v=u+at$

where: v = final velocity (speed) u = initial velocity (which is 0 m/s since it starts from rest) a = acceleration t = time

Since the acceleration is uniform, we can calculate it using the formula:

$a=\frac{2s}{t^2}$

where: s = distance t = time

Plugging in the values, we get:

$a=\frac{2\times 1000}{100^2}$ $a=0.2{\text{m/s}}^2$

Now we can use the equation of motion to find the final velocity:

$v=u+at$ $v=0+0.2\times 100$ $v=20\text{m/s}$

Therefore, after 100 seconds, the speed of the object will be 20 m/s.