Difference Between Speed And Velocity
- The ‘distance’ travelled by a body in unit time interval is called its speed. When the position of a body changes in particular direction, then speed is denoted by ‘velocity’. i.e. the rate of change of displacement of a body is called its Velocity.
- Speed is a scalar quantity while velocity is a vector quantity.
- ( text{Speed}=frac{text{distance}}{text{time}} )
- ( text{Velocity}=frac{text{displacement}}{text{time}} )
- Unit: In M.K.S. system = ms-1
In C.G.S. system = cm/s - If time distance graph is given then speed can be given by the slope of the line, at given time
( text{V}=frac{text{ }!!Delta!!text{ s}}{text{ }!!Delta!!text{ t}}=text{Slope} )
![velocity-time-graph]()
- The area of velocity time graph gives displacement travelled.
Types of speed
(a) Average and Instantaneous speed
Average speed: It is obtained by dividing the total distance travelled by the total time interval. i.e.
( text{Average speed}=frac{text{total},,text{distance}}{text{total},,text{time}} )
( text{Average},text{velocity}=frac{text{displacement}}{text{total},,text{time}} )
- Average speed is a scalar, while average velocity is a vector.
- For a moving body average speed can never be –ve or zero (unless t → ∞), while average velocity can be i.e
( >0text{ while }overset{to }{mathop}},>=or<text{ }0 ) - In general average speed is not equal to magnitude of average velocity. However it can be so if the motion is along a straight line without change in direction
- If a particle travels distances L1, L2, L3 at speeds v1, v2, v3 etc respectively, then
( =frac{Delta s}{Delta t}=frac++…..+}{frac}}+frac}}+….+frac}}}=frac{sum{Li}}{sum{frac}}}} ) - If a particle travels at speeds v1, v2 etc for intervals t1, t2 etc respectively, then
( =frac++….}++….}=frac{sum}}{sum}} )
Instantaneous speed: The speed of a body at a particular instant of time is called its instantaneous speed.
( =&#xnder;set{Delta tto 0}{mathop{lim }},,frac{Delta s}{Delta t}=frac{ds}{dt} )
(b) Uniform and Non uniform speed
Uniform speed: If an object covers equal distance in equal interval of time, then time speed graph of an object is a straight line parallel to time axis then body is moving with a uniform speed.
Non-uniform speed: If the speed of a body is changing with respect to time it is moving with a non-uniform speed.
Speed And Velocity Example Problems With Solutions
Example 1. The distance between two points A and B is 100 m. A person moves from A to B with a speed of 20 m/s and from B to A with a speed of 25 m/s. Calculate average speed and average velocity.
Solution: (i) Distance from A to B = 100 m
Distance from B to A = 100 m
Thus, total distance = 200 m
Time taken to move from A to B, is given by
( =frac{text{distance}}{text{velocity}}=frac{100}{20}=5text{ seconds} )
Time taken from B to A, is given by
( =frac{text{distance}}{text{velocity}}=frac{100}{25}=4text{ seconds} )
Total time taken = t1 + t2 = 5 + 4 = 9 sec.
∴ Average speed of the person
( =frac{text{Total},text{dis},text{tan},text{cecovered}}{text{Total},text{time},text{taken}}=frac{200}{9}=22.2text{ m/s} )
(ii) Since person comes back to initial position A, displacement will be zero, resulting zero average velocity.
Example 2. A car moves with a speed of 40 km/hr for first hour, then with a speed of 60 km/hr for next (1frac{1}{2}) half hour and finally with a speed of 30 km/hr for next hours. Calculate the average speed of the car.
Solution: Distance travelled in first hour, is given by
s1 = speed × time = 40 km/hr × 1 hr = 40 km
Distance travelled in next half an hour, is given by
s2 = speed × time = 60 km/hr × (frac { 1 }{ 2 }) hr = 30 km
Distance travelled in last (1frac{1}{2}) hours, is given by
s3 = speed × time = 30 km/hr × (frac { 3 }{ 2 }) hr = 45 km
Thus, total distance travelled = s1 + s2 + s3
= 40 + 30 + 45 = 115 km
Total time taken = 1 + (frac { 1 }{ 2 }) + (1frac{1}{2}) = 3 hours
Average speed = (frac { Total distance covered }{ Total time taken } ) = (frac { 115km }{ 3hrs })
= 38.33 km/hr
Example 3. Figure shows time distance graph of an object. Calculate the following :
(i) Which part of the graph shows that the body is at rest ?
(ii) Average speed in first 10 s.
(iii) Speeds in different parts of motion.
Solution: (i) The part BC shows that the body is at rest.
(ii) In first 10 seconds, distance travelled = 100m
( text{Average speed}=frac{text{total},,text{distance}}{text{total},,text{time}} )
( =frac{100}{10}=10text{ m/s} )
(iii) Speed of the object in part AB is given by slope = 100/6 = (frac { 50 }{ 3 }) m/s
Speed of object in part BC = 0 m/s
Speed of the object in part CD
( =frac{100-40}{12-10}=frac{60}{2}=30~text{m/s} )
Speed of object in part DE
( =frac{40-0}{14-12}=frac{40}{2}=30~text{m/s} )
Example 4. Time-velocity graph of a particle is shown in Figure. Calculate the distance travelled in first seconds.
Solution: Distance travelled in first 8s is given by area OABCG
= area of rectangle OAMG + area of triangle BMC
= 8 × 60 + (frac { 1 }{ 2 }) × 4 × 40
= 480 + 80 = 560 m.
Example 5. A cow walked along a curved path from P to Q, which is 70 m away from P. Q lies to the south-west of P. The distance travelled by the cow is 240 m and the time taken is 160 s.
Calculate the
(a) average speed,
(b) average velocity,
of the cow moving from P to Q.
Solution:
Total distance travelled = 240 m
Displacement = 70 m
Time taken = 160 s
