Question

0.00s	6.50m
0.25s	11.14m
0.50s	15.31m
0.75s	19.02.m
1.00s	22.25m
1.25s	25.02m
1.50s	27.31m
1.75s	29.14m
2.00s	30.50m
2.25s	31.39m
2.50s	31.81m
2.75s	31.77m
3.00s	31.25m
3.25s	30.27m
3.50s	28.81m
3.75s	26.89m
4.00s	24.50m
4.25s	21.64m
4.50s	18.31m
4.75s	14.52m
5.00s	10.25m

Astronauts on a distant planet toss a rock into the air. With the aid of a camera that takes pictures at a steady rate, they record the height of the rock as a function of time as given in the figures above.

(a) Find the average velocity of the rock in the time interval between each measurement and the next.

(b) Using these average velocities to approximate instantaneous velocities at the midpoint of the time intervals, make a graph of velocity as a function of time.

Answer 1

from given chart,

Time ( sec )	Height ( m )	Δh ( m )	Δt ( sec )	v ( m/sec )	Mid point time
0	6.5
		4.9	0.25	19.6	0.125
0.25	11.4
		3.91	0.25	15.64	0.375
0.5	15.31
		3.71	0.25	14.84	0.625
0.75	19.02
		3.23	0.25	12.92	0.875
1	22.25
		2.77	0.25	11.08	1.125
1.25	25.02
		2.29	0.25	9.16	1.375
1.5	27.31
		1.83	0.25	7.32	1.625
1.75	29.14
		1.36	0.25	5.44	1.875
2	30.5
		0.89	0.25	3.56	2.125
2.25	31.39
		0.42	0.25	1.68	2.375
2.5	31.81
		-0.04	0.25	-0.16	2.625
2.75	31.77
		-0.52	0.25	-2.08	2.875
3	31.25
		-0.98	0.25	-3.92	3.125
3.25	30.27
		-1.46	0.25	-5.84	3.375
3.5	28.81
		-1.92	0.25	-7.68	3.625
3.75	26.89
		-2.39	0.25	-9.56	3.875
4	24.5
		-2.86	0.25	-11.44	4.125
4.25	21.64
		-3.33	0.25	-13.32	4.375
4.5	18.31
		-3.79	0.25	-15.16	4.625
4.75	14.52
		-4.27	0.25	-17.08	4.875
5	10.25

v(m/sec) 0 / ਗਾਗਾਂ . 135 79 11 13 15 17 19 21 23 5 2 29 31 33 35 ਤੋਂ 39