Study the velocity-time graph and calculate.(i) the acceleration from

1.	Study the velocity-time graph and calculate.(i) the acceleration from A to B. (ii) the acceleration from B to C. (iii) the distance covered in the region ABE. (iv) the average velocity from C to D. (v) the distance covered in the region BCFE.
Answer» (i) Acceleration from A to B = \(\frac{change\,in\,velocity}{change\,in\,time}\)= \(\frac{25-0}{3-0}\)= 8.33 m/s² (ii) Acceleration from B to C = \(\frac{15-25}{4-3}\)= -10 m/s² (iii) Distance covered in the region ABE = \(\frac12\)× base × height = × 3s × 25 m/s = 37.5 m (iv) Average velocity from C to D = \(\frac{initial\,velocity\,+\,final\,velocity}{2}\) = \(\frac{15-0}{2}\)= 7.5 m/s (v) Distance covered in the region BCFE =\(\frac12\) × sum of parallel sides x distance between them =\(\frac12\) × ( 25+15) × 1 = 20 m

Study the velocity-time graph and calculate.(i) the acceleration from A to B. (ii) the acceleration from B to C. (iii) the distance covered in the region ABE. (iv) the average velocity from C to D. (v) the distance covered in the region BCFE.

Answer»

(i) Acceleration from A to B = \(\frac{change\,in\,velocity}{change\,in\,time}\)= \(\frac{25-0}{3-0}\)= 8.33 m/s²

(ii) Acceleration from B to C = \(\frac{15-25}{4-3}\)= -10 m/s²

(iii) Distance covered in the region ABE = \(\frac12\)× base × height

= × 3s × 25 m/s = 37.5 m

(iv) Average velocity from C to D = \(\frac{initial\,velocity\,+\,final\,velocity}{2}\)

= \(\frac{15-0}{2}\)= 7.5 m/s

(v) Distance covered in the region BCFE =\(\frac12\) × sum of parallel sides x

distance between them =\(\frac12\) × ( 25+15) × 1 = 20 m