Question

A object of mass 2kg moving with speed of 10m/sec changes it's speed to 15m/sec in 2sec find acceleration force and impulse

Answer 1

Acceleration = 2.5 m/s$^2$ Force = 5 N Impulse = 10 Ns

Answer 2

The problem asks to find the acceleration, force, and impulse for an object given its mass, initial speed, final speed, and the time taken for the speed change.

1. Acceleration ($a$): We use the first equation of motion, $v = u + at$, where $v$ is the final speed, $u$ is the initial speed, and $t$ is the time.
2. Force ($F$): Assuming a constant force causing the change in speed, we use Newton's second law of motion, $F = ma$, where $m$ is the mass and $a$ is the acceleration.
3. Impulse ($J$): Impulse is defined as the change in momentum. The initial momentum is $p_i = mu$ and the final momentum is $p_f = mv$. The impulse is $J = p_f - p_i = mv - mu$. Alternatively, impulse is also the product of the force and the time interval over which it acts, $J = F \Delta t$.

Given: Mass, $m = 2$ kg Initial speed, $u = 10$ m/s Final speed, $v = 15$ m/s Time, $t = 2$ s

1. Acceleration: $v = u + at$ $15 = 10 + a \times 2$ $15 - 10 = 2a$ $5 = 2a$ $a = \frac{5}{2} = 2.5$ m/s$^2$

2. Force: $F = ma$ $F = 2 \text{ kg} \times 2.5 \text{ m/s}^2$ $F = 5$ N

3. Impulse: Using change in momentum: $J = mv - mu$ $J = m(v - u)$ $J = 2 \text{ kg} \times (15 \text{ m/s} - 10 \text{ m/s})$ $J = 2 \text{ kg} \times 5 \text{ m/s}$ $J = 10 \text{ kg} \cdot \text{m/s}$ Alternatively, using force and time: $J = F \Delta t$ $J = 5 \text{ N} \times 2 \text{ s}$ $J = 10 \text{ Ns}$ Note that 1 Ns is equivalent to 1 kg$\cdot$m/s.