The position of a moving car at time t is given by f(t)=at²+bt+c, t>0, where a,b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t?,t?] is attained at the point:
The position of a moving car at time t is given by f(t)=at²+bt+c, t>0, where a,b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t?,t?] is attained at the point:
Option 1 -
(t₂-t₁)/2
Option 2 -
a(t₂-t₁)+b
Option 3 -
(t₁+t₂)/2
Option 4 -
2a(t₁+t₂)+b
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1 Answer
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Correct Option - 3
Detailed Solution:Average speed = (f (t? )-f (t? )/ (t? -t? ) = a (t? +t? )+b.
Instantaneous speed = f' (t)=2at+b.
2at+b=a (t? +t? ) ⇒ t= (t? +t? )/2.
Similar Questions for you
16cos2θ + 25sin2θ + 40sinθ cosθ = 1
16 + 9sin2θ + 20sin 2θ = 1
+ 20sin 2θ = 1
– 9cos 2θ + 40sin 2θ = – 39
48tan2θ + 80tanθ + 30 = 0
24tan2θ + 40tanθ + 15 = 0
-> ,
So will be rejected as
Option (4) is correct.
12x =
is the solution of above equation.
Statement 1 is true
f(0) = – 1 < 0
one root lies in , one root is which is positive. As the coefficients are real, therefore all the roots must be real.
Statement 2 is false.
tan2 A = tan B tan C
It is only possible when A = B = C at x = 1
A = 30°, B = 30°, C = 30°
a = sin−1 (sin5) = 5 − 2π
and b = cos−1 (cos5) = 2π − 5
∴ a2 + b2 = (5 − 2π)2 + (2π − 5)2
= 8π2 − 40π + 50
sin 2 + tan 2 > 0
Let tan = x
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