What is the displacement of a car in 30 seconds if it is Travelling with a velocity of 15m s?

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This displacement calculator finds the displacement (distance traveled) by an object using its initial and final velocities as well as the time traveled. The average velocity of the object is multiplied by the time traveled to find the displacement. The equation x = ½( v + u)t can be manipulated, as shown below, to find any one of the four values if the other three are known.

Displacement Equations for these Calculations:

\( s = \dfrac{1}{2}( v + u )t \)

Where: s = displacement v = final velocity u = initial velocity

t = time

Different resources use slightly different variables so you might also encounter this same equation with vi or v0 representing initial velocity (u) and vf representing final velocity (v) such as in the following form:

\( s = \dfrac{1}{2}( v_f + v_i )t \)

Where: s = displacement

vf = final velocity

Displacement calculations used in calculator:

Solving for the different variables we can use the following formulas:

• Given v, u and t solve for s
  Given initial velocity, final velocity and time calculate the displacement.
• Given s, t and u solve for v
  Given displacement, time and initial velocity calculate the final velocity.
• Given s, t and v solve for u
  Given displacement, time and final velocity calculate the initial velocity.
• Given v, u and t solve for s
  Given initial velocity, final velocity and time calculate the displacement.

Displacement Problem 1:

A car traveled down a road for 45 seconds. The car turned onto the street at 20 m/s and by the end of the street it was traveling 23 m/s. How long is the street?

Since we were given the initial velocity (20 m/s), the final velocity (23 m/s), and the time (45 seconds) the equation can be directly applied. s = ½(20+23)*45= 967.5 meters

Displacement Problem 2:

When a pitcher throws a pitch from the pitcher's mound, he is about 60 feet from home plate. If the ball leaves his hand at 132 ft/s and reaches home plate with a speed of 110 ft/s, how long does it take the ball to travel from the mound to home plate?

In this problem we are given a different set of values. The equation s = ½( v + u )t can be algebraically manipulated to t = 2s/(v+u). The displacement is 60 feet, the initial velocity is 132 ft/s and the final velocity is 110 ft/s.

t = 2(60 ft)/(132+110 ft/s)= 0.496 seconds

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Science for Class 8 - Part 1>Motion>Let us assess>Q 9

1. Rest and Motion:

(i) Reference object is the object with respect to which the state of motion or state of rest of another object is described.

(ii) When a body does not change its position with respect to time and a reference point, it is said to be at rest with respect to that reference point.

(iii) When the position of a body continuously changes with respect to the time and a reference point it is said to be in a state of motion.

2. Distance and Displacement:

(i) Distance is the actual length of the path travelled by a moving body, irrespective of the direction in which the body moves. It is a scalar quantity.

(ii) The straight line distance between initial and final position. It has both magnitude and direction. It is a vector quantity.

(iii) The SI unit of both distance and displacement is metre.

3. Speed and Velocity:

(i) Speed is the distance travelled by a body in unit time. It is a scalar quantity and its SI unit is m/s.

(ii) Velocity is the displacement covered by a body in a unit time in a specified direction. It is a vector quantity and its SI unit is m/s.

(iii) If a body in motion covers equal distances in equal intervals of time, the body is said to have uniform speed. If it covers unequal distances in equal intervals of time, the body is said to have non-uniform speed.

(iv) Average Speed=total distance travelledtime taken to travel the distance

(v) A body has uniform velocity if it covers equal displacements in the same direction in equal intervals of time.

4. Acceleration:

(i) Acceleration is the rate of change of velocity. It has the unit m/s2.

(ii) Acceleration can be calculated as a=change in velocitytime=(v-u)t, where v is the final velocity, u is the initial velocity and t is the time. It is a vector quantity.

(iii) Negative acceleration is known as retardation. The velocity of a retarding body decreases with time.

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