an object accelerates uniformly along a straight line from a velocity of 10ms-1 until 25ms-1 in 5s.

a)the velocity of the object during the first 10s of motion
b)the time taken to reach a final velocity 50ms-1

V = 10 + 3 t

Initial velocity U=10m/s

Final velocity V=25m/s
Velocity V= 25m/s-10m/s=15m/s
Time t=5s
(a) In 5s, the velocity v= 15m/s.
In 10s, the velocity
v= 15m/s×2=30m/s.
(b) V=50m/s a=dv/t=15m/s÷5s=3m/s^2
V=u+at
50m/s=10m/s+(3m/s^2×t)
50m/s=10+3t
50-10=3t
40=3t
t=40/3=13.666
Thus, t=13.67s.

To solve both parts of the question, we need to first calculate the acceleration of the object by using the formula:

Acceleration (a) = Change in velocity (Δv) / Time taken (Δt)

Given that the object accelerates uniformly from a velocity of 10 m/s to 25 m/s in 5 seconds, we can calculate the acceleration:

Δv = 25 m/s - 10 m/s = 15 m/s
Δt = 5 s

a = Δv / Δt = 15 m/s / 5 s = 3 m/s²

Now, let's proceed to answer each part of the question:

a) The velocity of the object during the first 10 seconds of motion:
Since we know that the object accelerates uniformly, we can use the following equation to find the velocity:

Velocity (v) = Initial velocity (u) + Acceleration (a) * Time (t)

Given:
Initial velocity (u) = 10 m/s
Acceleration (a) = 3 m/s²

To find the velocity during the first 10 seconds, we substitute these values into the equation:

v = u + at
v = 10 m/s + 3 m/s² * 10 s
v = 10 m/s + 30 m/s
v = 40 m/s

Therefore, the velocity of the object during the first 10 seconds of motion is 40 m/s.

b) The time taken to reach a final velocity of 50 m/s:
We can use the same equation as before to find the time taken (t):

v = u + at

Given:
Initial velocity (u) = 10 m/s
Acceleration (a) = 3 m/s²
Final velocity (v) = 50 m/s

Rearranging the equation to solve for t:

t = (v - u) / a
t = (50 m/s - 10 m/s) / 3 m/s²
t = 40 m/s / 3 m/s²
t ≈ 13.33 s

Therefore, the time taken to reach a final velocity of 50 m/s is approximately 13.33 seconds.