1.A body with an initial velocity of 18km/hr accelerates uniformly at the rateof 9cm/sec2over a distance of 200m.Calculate, a)the acceleration in m/sec2 b)its final velocity in m/s

2.The distance travelled by a body moving with uniform acceleration in the nth second is given by Sn=3.8+0.4n,find the velocity of the body .

1.

vₒ = 18 km/hr = 18000/3600 = 5 m/s.
a = 9 cm/s² = 0.09 m/s².
s =(v² - vₒ²)/2•a.
v = sqrt (vₒ² +2•a•s) = sqrt(25 +2•0.09•200) =7.81 m/s.

2.

Distance traveled by a body in nth second is
Sn = u + (2n-1)•a/2.
If you know acceleration "a" you can find velocity "u"

sqrt=square root=quadratic root=second root

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To solve both questions, we will use the equations of motion for uniformly accelerated motion.

1. Let's first solve for part (a), which asks for the acceleration in m/sec².

Given:
Initial velocity (u) = 18 km/hr
Acceleration (a) = 9 cm/sec²
Distance (s) = 200 m

We know that acceleration is the rate of change of velocity with respect to time. Therefore, we need to convert the initial velocity and acceleration to m/s.

Converting initial velocity:
Initial velocity (u) = 18 km/hr
1 km = 1000 m, 1 hr = 3600 s (conversion factors)
u = 18 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 5 m/s

Now we can calculate the acceleration:
Acceleration (a) = 9 cm/sec²
1 cm = 0.01 m, (conversion factor)
a = 9 cm/sec² * 0.01 m/cm = 0.09 m/sec²

Therefore, the acceleration is 0.09 m/sec².

Now, let's solve for part (b), which asks for the final velocity in m/s.

We can use the equation of motion:
v² = u² + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
s = distance

Substituting the given values:
v² = (5 m/s)² + 2 * (0.09 m/sec²) * (200 m)
v² = 25 m²/s² + 36 m²/s²
v² = 61 m²/s²

Taking the square root of both sides:
v = sqrt(61) m/s ≈ 7.81 m/s

Therefore, the final velocity is approximately 7.81 m/s.

2. For the second question, we are given the distance traveled in the nth second, Sn = 3.8 + 0.4n. We need to find the velocity of the body.

The distance traveled in the nth second is equal to the average velocity * time.
So we can set up the equation:
Sn = average velocity * time

Given:
Sn = 3.8 + 0.4n

Since the average velocity is the change in distance divided by the change in time, we can differentiate the equation to find the velocity.

Differentiating Sn with respect to time:
v = d(Sn)/dt
v = d(3.8 + 0.4n)/dt
v = 0.4

Therefore, the velocity of the body is 0.4 m/s.

Vo = 18km/h =18000m/3600s=5m/s=Initial

velocity.

1a. a =9cm/s^2 * 0.01m/cm = 0.09 m/s^2.

1b. V^2 = Vo^2 + 2ad
V^2 = 5^2 ++ 0.18*200 = 61
V = 7.81 m/s. = Final velocity.

what is "sqrt" please can i know?????